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# Some explicit identities associated with positive self-similar Markov processes.

Abstract : We consider some special classes of Lévy processes with no gaussian component whose Lévy measure is of the type $\pi(dx)=e^{\gamma x}\nu(e^x-1)\,dx$, where $\nu$ is the density of the stable Lévy measure and $\gamma$ is a positive parameter which depends on its characteristics. These processes were introduced in \cite{CC} as the underlying Lévy processes in the Lamperti representation of conditioned stable Lévy processes. In this paper, we compute explicitly the law of these Lévy processes at their first exit time from a finite or semi-finite interval, the law of their exponential functional and the first hitting time probability of a pair of points.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-00167291
Contributor : Juan Carlos Pardo Millan Connect in order to contact the contributor
Submitted on : Friday, August 17, 2007 - 5:30:52 PM
Last modification on : Tuesday, November 16, 2021 - 4:54:56 AM
Long-term archiving on: : Friday, April 9, 2010 - 12:54:22 AM

### Files

finckp1.pdf
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### Identifiers

• HAL Id : hal-00167291, version 1
• ARXIV : 0708.2383

### Citation

Loic Chaumont, Andreas Kyprianou, Juan Carlos Pardo Millan. Some explicit identities associated with positive self-similar Markov processes.. 2007. ⟨hal-00167291⟩

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